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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 506, page id 851387705:0526
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E C Y OL OIDF.
Angulis semiciculis sire superticiebus semieylindricis cirea axem A F incellixan-
cur cocidem linex rectae vel luperticies planae plano C A V ad angulos reclos polita
acque ab eo bisectae;) acque deinde in recta R u qua lir bali AD perpendicularis
SUIALUE (PFOPECE CUPVaTITaM) uE C F ad P A, (hoc cA, ut Diameter ad Semipe
ripheriam cireulis) sic ~_ ad x K, (qua nempe ratione dividendus est axis Cemi-
cireuli ue habeatur Semiperipherix cencrum gravitatis:) Frir a centrum graricacis
Solidi ex Ceniconvertione Frapezii V B, P circa rectam AF.
44. Cencrum aurem grariraris solidi ex semiconvertione Prianguli, habetur, B
a rectae LZ puncto FI, quod jam incellisatur ableindere rectam PHI, quae lic ad
FZ, ut 3 ad 4, (quod nempe cencrum graritatis cHet L dCWIETCCUE CUEVATITA,
verpendicularis Fn incellisatur (propter curraturam) ita diridi in p uc modo di
vilimus IEn in ~. Eru ucique e cenerum gravitaris tolidi ex semiconrertione Pri
ansuli v F P circa rectam A F. (Ouamquam revera perinde omnino elt ad hoc
negorium an omnino reperiantur puncta e, e, an cancum puncta H, FI: Nam ea-
dem est distancia, quancum ad reccam CF, punctorum K e P, irem punctorum I)
ec p: _ quancum ad rectam AF, eadem talcem dictanciarum rario, live puneta
IE, FI, Circ ae, 8, Considerentur.)
45. Cum igitur rario distantiarum lire punctorum K, FI, sive a, P, L recta AF,
lic uF +8 ad3, Lire 28ad30, rel 14 ac 25; ee magnicudinum, ut 5 ad 2: Prit,
qua ex his componitur, racio momentorum, uc 70 ad 30, live 7 ad 3. Quod cum
ubique tiac; caclem erit sc ratio momenti lolidorum ex semi convertione Frape.
Ziorum omnium ad omnium Friangulorum sIC COnVerIOTUM MOMenEI, HOC est.
momenti Colidi ex lemiconrertione senriereloidis, ad momeneum solidi ex sevy-
conrertione semicireulis (circa rectam AP, ) respectu rectae A F: NTempC vC7 ad
3. Onde collisencur puneta, t, 0, s, uc supra. Nempe si incellisatur ( cencrum
praricatis Folidi ex semiconvertione cireuli circa rectam AF, (gnod punctum C
dari supponimus, vel, si exigatur, deinceps exhribebimus 556;) ec tiac, ut 3 ac
sie FG ad PF; et deinde, uc5 ad 2, lic P P ad Fa; aeque ducatur as bali paral-
lela; eric cencum gravicatis solidi ex lemiconverlione lemiercloidis cirea rectum
AD, in recta 4d.
46. Cum rero distantia puncti sive R sive e a recta CF Fit 22. = 20ZZ; acque
distancia puncti H vel ae ab eadem recta lic 3Z.V; (quorum utrunque ex dictis
Patet:) erie diltanciarum racio, uc ZZ F 20 2 L ad3Z Y, EIre nC 2022. + 14. 2. L
ad [5 Z T. Oux si cum ratione magnitudinum 5 ad 2 componatur, habecur mo-
MEnTOTUM FatIO 100Z Z f 7OZ Y act 302Y, Sive 102Z F7Z X ad 32 L. Quod
cum ubique tiac; pro ratione momenei lolidi ex convertione (vel semiconvertione)
semieycloidis, ad momentum tolidi ex convertione (vel semiconvertione) lemi
circuli cirea rectam AP, respectu linea aequilibrii CF, sumenda erie cum racio
ad 3 (Propier 7 2. Z ad 32L) cum (Propier 10ZZ. ad 3Z L) ea ratio quam
habet decuplum momenei solicorum ex conrertione Prianoulorum oF pCicCA A F,
luspentorum in diltantiis Z Z respectire, ad triplum momenci corundem Colidorum
suspensorum in distantiis Z T: NemDC Ut Z RP3 = 3~R P ad ZR3 P, SIVC UE
(5A F9 = 2OOF q ad + C F 9. (Ouod 5 87 de Segg. Tusius declaratur. ) OuX
quidem ratio si cum ratione 7 ad 3 conjunsatur, habecur racio momenci (respectu
rectae C F) solidi ex convertione (vel semiconvertione) semicycloidis cirea re
Etam AP, ad momentum solidi ex simili convertione (rel semiconvertione) seni-
circuli: Nempe Z- R P3- 16R3D ad Z R3P, SiVC ut 45 P Z -- 5CZR ~ ad, FO2R2
HIOcCst, uc 45 A F 9 = 32 GF9ad +2CIF 9.
47. Si itaque ponamus Ce F, distanciam cenri graricaris solidi ex ea conversione
rel lemiconrersione semicireuli, (d recta C F;) de tar, ut 22 C F9 ad 45 AF9
32 C F9, lic GF ad GC; ierumque, ue 5 ad 2, Sic G 0 ad CeF; et duCaTUN F)
parallela rectae C F: Fric lemisolidi ex convertione (hoc est sosidi ex tergicon.
rertione) Semicyeloidis cirea rectam AF, cencrum graritatis in recta Py; adeo
que in ipsius eo puncto ubi occurricur recta as modo inventa 545. (Deligno-
mus autem in schemare cencrum graricacis in ea semiercloide, ubi minor ficura
centrum elset linearum contusio; perinde enim ad rem est, in vira defignetur.)
42. Flabito aurem centro gravitatis in lemilolido, d Forciori in Tolido interro
tecri cir- haberi cerrum est: puca in Aris punctor.
40. Louen n procestu (mutaris mutan , ut TuprA B 3T.) colligitur cen
icum scaricatis temilelidi ex conversione lei nemi ED C. F ciea rectam AP; e
conse
Duam
um
dinan
in
Colidi in-
AF.